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A new test methodology based on structural resonance
for mode I fatigue delamination growth in an
unidirectional composite
Irène Maillet, Laurent Michel, Germain Rico, Mathieu Fressinet, Yves
Gourinat
To cite this version:
Irène Maillet, Laurent Michel, Germain Rico, Mathieu Fressinet, Yves Gourinat. A new test
methodol-ogy based on structural resonance for mode I fatigue delamination growth in an unidirectional
compos-ite. Composite Structures, Elsevier, 2013, vol. 97, pp. 353-362. �10.1016/j.compstruct.2012.10.024�.
�hal-00824178�
This is an author-deposited version published in:
http://oatao.univ-toulouse.fr/
Eprints ID: 8072
To link to this article: DOI:
10.1016/j.compstruct.2012.10.024
URL:
http://dx.doi.org/10.1016/j.compstruct.2012.10.024
To cite this version:
Maillet, Irène and Michel, Laurent and Rico, Germain
and Fressinet, Mathieu and Gourinat, Yves A new test methodology based
on structural resonance for mode I fatigue delamination growth in an
unidirectional composite. (2013) Composite Structures, vol. 97 . pp.
353-362. ISSN
0263-8223
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A new test methodology based on structural resonance for mode I fatigue
delamination growth in an unidirectional composite
I. Maillet
a,⇑, L. Michel
a,⇑⇑, G. Rico
b, M. Fressinet
b, Y. Gourinat
a aUniversité de Toulouse, INSA, UPS, Mines Albi, ISAE, ICA (Institut Clément Ader), 10 av. Edouard Belin, BP 54032, 31055 Toulouse, France
b
DGA Techniques Aéronautiques, 47 rue St. Jean, BP 93123, 31131 Balma, France
Keywords:
Fiber reinforced polymer matrix Delamination resistance Mode I loading
Resonance test development Vibratory fatigue
Frequency effect
a b s t r a c t
A specific device has been set up to test by vibration resonance the mode I fatigue delamination growth onset of composite laminates. This test system, based on the DCB test specimen, is a mass-spring-spec-imen dynamic system designed to resonate. The defined operating conditions allow performing delami-nation propagation tests under imposed load and stopping the test under reproducible conditions, identical to the ones recommended in the ASTM-D6115 standard. This system allows fatigue tests to be driven up to 100 Hz, reducing the time taken by a factor of ten without detrimental heat being gen-erated in the material. The effect of frequency on the fatigue delamination growth on mode I has been investigated through a comparison with standard tests performed at 10 Hz. A decrease in resistance to the propagation of delamination is observed with the increase in frequency for the composite studied. This frequency effect seems to be a strain rate effect and was taken in consideration by using dynamical critical energy restitution rate for the G–N curve plotting.
1. Introduction
Due to their lightness and stress adaptability, composite mate-rials are more and more used in the aeronautical frame. Aeronau-tical structures are submitted to vibrations during their service life due to aerodynamic turbulent flow around the structure. In this sonic fatigue domain applied loads remain low, but performed at high frequency a great number of cycles can be reached within a
short time[1]. Damage tolerance policy should address any risk
of delamination propagations within the whole service life of
air-planes[2]. Even if the sonic fatigue case is not the major design
problem, investigation of knowledge of composite material behav-ior under high cycle fatigue seems to be of sufficient importance to be addressed.
A delamination will propagate under a combination of the three pure modes: opening mode (mode I), sliding mode (mode II) and tearing mode (mode III). Pure modes I and II tests are generally
used to characterize composite material in fatigue[3–6]. For the
more critical mode, the mode I, the ASTM defined the Double
Can-tilever Beam (DCB) test as a standard[3]. This DCB fatigue test is
achieved at a frequency of 10 Hz, with a controlled loading ratio
and a test stop condition linked to the specimen compliance. Then
fatigue behavior of carbon/epoxy laminate in pure mode I up to 106
cycles has been widely studied[7,6,8]. At this frequency the
dura-tion of test needed to reach 106cycles is more than 11 days. In
these conditions exploration of the high cycle fatigue field cannot be considered. Indeed delamination propagation under pure mode of composite material laminates at high frequency to reach high cycle fatigue still seems not to be addressed in the literature.
In the frame of accelerated fatigue tests, new test methodolo-gies were developed in order to increase frequency of tests, applied
mainly for metallic materials. George et al.[9]designed vibration
fatigue test under resonance conditions to represent uni-axial and bi-axial bending loadings of turbine blades. They used a finite element model to design a suitable plate specimen and tested it to determine the endurance limit with the Maxwell and Nicholas
method [10]. In this method, the specimen is loaded by stress
steps, each step corresponding to the number of cycles of the
esti-mated endurance limit (around 106 cycles). The tests are
per-formed on a shaker at frequencies around 1000 Hz, and at a
stress ratio of ÿ1, allowing to reach 106cycles within a few hours.
Bathias[11,12]developed a piezoelectric fatigue machine working
at 20 kHz or 30 kHz for tension–compression test and three-point bending test at different loading ratios. Those tests are mostly used to observe the metallic behavior in gigacycle fatigue in different
environment conditions[13–15].
For organic matrix composite materials mechanical behavior is very sensitive to frequency. Frequency effects can be divided in ⇑Corresponding author. Tel.: +33 (0) 561339195; fax: +33 (0) 561339095.
⇑⇑Principal corresponding author. Tel.: +33 (0) 561339141; fax: +33 (0) 561339095.
E-mail addresses: irene.maillet@isae.fr (I. Maillet), laurent.michel@isae.fr (L. Michel).
three competitive parts[16,17]: a creep effect in the low frequency domain (below 10 Hz), a strain rate effect in the high frequency do-main and the self generated heating due to the low thermal con-ductivity of the material most likely to appear at elevated loading frequencies.
Wang et al.[18]used a piezoelectric ultrasonic fatigue machine
to test in gigacycle regime crack growth in bonded composite re-pairs of notched metallic plates as a function of the number of patch plies. The patches were in boron-epoxy and their ability to delay the crack propagation in a notched aluminum alloy specimen was investigated. No mention of temperature observation during tests was reported despite the very high load frequency.
Other authors were interested in high cycle fatigue of
compos-ite material. Michel et al.[19] studied the AS4/PEEK in tension,
compression and bending. For tension and compression tests: on hydraulic test machine for low and medium cycle fatigue
test in the frequency range of 0.5–10 Hz, and
on electromechanical resonance machine for high cycle and gigacycle regime in the range of 57–158 Hz. These tests were conducted at room temperature with a cooling air flow allowing the specimen surface temperature to remain below 45 °C. Three-points bending tests were performed with the help of a servo-hydraulic actuator between 0.5 Hz and 10 Hz for low cycle regimes and at 50 Hz for high ones without cooling system.
In this study for most of the tests the material fatigue behavior was found to follow a log linear law independent of the frequency: results for high frequency ranges were consistent with the ones at low frequencies. For pure compression case, results seem however to be sensitive to frequency. Although the specimen temperature during tests remained far below the glass temperature of the PEEK matrix, the authors assigned this behavior to a local buckling of fibers due to the temperature induced softening of the matrix.
Hos-oi et al.[20,21]investigated the influence of transverse cracks on
delamination initiation and propagation in CFRP during tensile fatigue test. All the tests were conducted with an hydraulic testing machine. For high cycle fatigue, the test frequency was 100 Hz with low applied load to limit the temperature rise to 10 °C. Within this condition the authors ensured there was no temperature effect in their results.
The aim of this work is then to implement a suitable test meth-odology to investigate the mode I propagation threshold for a large number of cycles. As the DCB specimen is loaded under bending, it requires consequent displacements: a minimum dis-placement of 1 mm for the Energy Restitution Rate range tested in our study. As it is difficult to reach at the same time high fre-quency and large displacement with classical machines, an accel-erating testing device has been designed and fixed on a shaker. The device principle is based on resonance of mass-spring-specimen system and allows to perform tests at 100 Hz, hence reducing the time taken by a factor of ten, as compared to conven-tional tests. A standard CFRP laminate widely used in aeronautical domain is then characterized with the new apparatus and the results compared with a classical characterization: at medium fre-quency (10 Hz).
2. Classical characterization 2.1. Material specimen and facilities
Specimens used are unidirectional composite beams made of 20 plies of T700/M21 (HexcelÓ). The beam specimens were cut out from a press manufactured plate. The curing cycle followed a standard cycle with an homogenization stage as recommended
by HexcelÓ. A 25
l
m thickness Teflon film is inserted in themid-plane of the laminate during the manufacturing to create an
ini-tial crack. It is larger than the standards’ recommended 13
l
m[22], but all the specimens were pre-cracked in mode I loading
to get at least a 2 mm delamination extension before the fatigue tests.
The specimen dimensions conform to the standard ASTM
D5528 [22] of the delamination propagation test in mode I
(L ¼ 180 mm; b ¼ 25 mm; h ¼ 2:5 mm; a0¼ 50 mm Fig. 1) It is
instrumented with a RUMULÓ crack gauge to follow the crack propagation during tests. The load is applied by the means of load-ing blocks stuck on both sides of the specimen. The loadload-ing block
section dimension is 10 10 mm2. (Fig. 2).
The tests were performed on a servo-hydraulic machine equipped with a 1 kN load–capacity cell. The parameters measured and used for the data reduction were the opening displacement, the crack extension and the load.
2.2. Specimen compliance law and resistance
Preliminary mode I interlaminar fracture toughness tests were conducted for various crack sizes to determine the propagation
values of fracture toughness GIpand the master compliance curve
of the specimen. This curve links the specimen stiffness to the delamination size.
The static compliance law is then (Fig. 3).
C ¼ C0 an ð1Þ
where C is the compliance and a is the measured crack length:
C0¼ 4:28 eÿ7and n ¼ 2:83
Some authors found that carbon/epoxy materials are rate
sensi-tive[23]. In order to investigate loading rate effects on the Energy
Restitution Rates (ERR) in pure mode I, several tests where per-formed. The cross head speed was controlled at 0.01 mm/s (follow-ing the ASTM standards) for four specimens and at higher speeds for others (from 5 mm/s to 150 mm/s).
The ERR is calculated with the compliance method (Eq. (2))[22].
G ¼nPd2ba ð2Þ
where G is the ERR, P the load, d the opening displacement and b the width of the specimen.
All the specimens were found to follow the same compliance
law (Fig. 3on the left). After analyze two distinct propagation
en-ergy restitution rates in mode I are found: GIsta
p ¼ 400 N=m for the
lower loading rates and GIdyn
p ¼ 300 N=m for higher ones (Fig. 3on
the right).
2.3. Classical DCB fatigue test 2.3.1. Test conditions
DCB fatigue tests have been performed at a controlled displace-ment ratio of R ¼ 0:1 and a frequency of 10 Hz following the
stan-dard requirements[3].
2.3.2. Data reduction
The fatigue compliance is assumed to follow the static
compli-ance law (Eq. (1)). The ERR is then calculated with the compliance
method (Eq. (3))[22].
Gmax¼
nPmaxdmax
2ba ð3Þ
where Gmaxis the maximal ERR reach during a cycle, Pmaxthe
max-imal load and b the width of the specimen.
G–N curve. Six specimens were used to determine the G–N onset propagation curve which links the ERR and the number of cycles to the propagation onset.
The G–N curve is then plotted and the parameters determined (Fig. 4):
Gmax¼ p Nmc ð4Þ
where Ncis the number of cycles necessary to reach the
propaga-tion threshold value. It is defined as the number of cycles until
the compliance has increased by 5% by the ASTM D6115[3].
Although this method is the one recommended by the ASTM, most of the authors used the Paris law to characterize
delamina-tion propagadelamina-tion in fatigue. Brunner et al.[4] even proposed a
new standardized procedure of interlaminar delamination propa-gation in mode I to take this into account.
Paris law. Three specimens were used to identify the relation
between the crack speed da
dN
ÿ
vs the ERR (G): the Paris law (Eq.
(5)). It has been chosen to use dimensionless value by dividing
ERR by the propagation ERR GstatIp
. da dN ¼k Gmax Gstat Ip !n ð5Þ
where N is the number of cycles.
The Paris curve obtained presents a classical linear variation with deviations for the highest and lowest ERR ratios of the testing
range (highlighted by dashed lines on the graph5). A no
propaga-tion threshold can be estimated around 140 ± 15 N/m taking into account the measurement accuracy.
Results from the different specimens clearly follow a Paris law which is then found to be independent of the propagation length (Fig. 5). It should be noted that this length necessary to cover the whole range of Paris curve is fairly limited: no more than 22 mm. With this short crack extension, no fiber bridging was observed during fatigue tests. Any change in compliance is then directly linked to the delamination extension rather than to any process zone increase.
So the G–N onset propagation curve can be extrapolated from the Paris test results by dividing the total propagation into seg-ments, each one linked to one propagation threshold. The number of cycles used to determine the threshold value is defined as the number of cycles until the compliance has increased by 5% as it
was used for the test before (Fig. 5).
Fig. 2. Test specimen according to ASTM D5528 with electrical crack gauge.
Fig. 3. T700/M21 compliance and resistance curves.
The total length of propagation is so divided into segments of length needed to increase the compliance of the specimen of 5% (Fig. 6a). For each first point of segment, the ERR is calculated with
the compliance method (Eq. (3)). The number of cycles needed to
propagate the delamination from the first point to the last point
of the segment is then determined (Fig. 6b). This data are used to
plot the G–N propagation curve point by point (Fig. 6c).
The delamination growth onset curve found is close to the one
plotted with standard results (Fig. 7). The G–N propagation curve
obtained by the Paris test process is then appropriate and saves a lot of test time. Considering the graph for the low number of cycles, the G–N curve deviates from the main slope for the highest ERR. Its intersection with the vertical axis illustrated by the dashed line represents an equivalent static ERR. This threshold value for one cycle between 300 N/m and 350 N/m is consistent with the static
resistance curve (Fig. 3) and the Paris data (Fig. 5). On the other
hand, the no propagation threshold does not appear on the G–N
curve. In this propagation range the compliance variation is very small so the data reduction does not allow to represent it. 3. Dynamical fatigue test
3.1. Test conditions 3.1.1. System presentation
The dynamic tests use resonance and are conducted using a shaker. The device looks like an inertial tension–compression ma-chine (Fig. 8).
The dynamic representation of the global system is a mass-spring system, where the specimen is represented by its opening
stiffness ðKEÞ. A spring (stiffness KR) is connected in parallel with
the specimen; the compression length of the spring ðMlÞ allows to fix the initial opening of the specimen ðdÞ which determines
the average loading level ðFmeanÞ (Part3.2.1).
Fig. 5. Normalized Paris Law at 10 Hz and R ¼ 0:1.
Fig. 6. Curve treatment to plot G–N curve.
Fig. 7. G–N onset propagation curve standard and Paris method at 10 Hz and R ¼ 0:1.
During the experiment, the shaker generates a sinusoidal accel-eration which sets the mass, M, in motion and thus loads the spec-imen around its equilibrium position. The loading frequency is chosen equal to the resonance frequency of the global system in or-der to take advantage of the amplification factor due to resonance. The resonance frequency of the system depends on the mass, the specimen opening stiffness and the spring stiffness. The spring stiffness has to be lower than the specimen one to allow a precise opening adjustment. In order to obtain a high frequency, the mass has to be as light as possible and the opening stiffness as high as possible.
The cycling regulation at constant amplitude ðFampÞ is
per-formed by the control of the mass M acceleration (Part3.2.2).
(Fig. 9).
The load ratio R is completely determined by Fmeanand Famp:
R ¼FFmin max¼
Fmeanÿ Famp
Fmeanþ Famp ð6Þ
Dynamical fatigue tests are performed at a controlled load ratio of R ¼ 0:1 and at a frequency of 100 Hz (for the loading device and the specimen described below).
3.1.2. Dynamic specimen design
A specific specimen was designed for the dynamic tests. It is based on the standard DCB specimen. However to be adapted to the dynamic test constraints, the crack and the specimen lengths
were modified (L ¼ 80 mm; b ¼ 25 mm; h ¼ 2:5 mm and
a0¼ 30 mm, Fig. 1). The dimensions of the loading blocks were
the same as for the classical specimens. It was checked that the shortness of the initial crack length compared to the standard requirements does not necessitate any correction for the ERR calculation.
The first bending mode of the beam must not disturb the dynamics of the system, so this resonance mode was pushed above 100 Hz. Indeed, the specimen has to be as rigid as possible in bend-ing: it was decided to keep a thickness of 5 mm, but the total length of the dynamical specimen was reduced to 80 mm in order to get a 1st mode up to 500 Hz.
As the opening stiffness of the specimen is strongly linked to the system resonance frequency, the initial crack size should be re-duced to lead to the highest possible frequency for the system. But the Energy Restitution Rate (ERR) is very sensitive to the crack size which has to be precisely measured. To determine the speci-men length, the ERR uncertainty was calculated based on measure-ment instrumeasure-ment precision and the adjustmeasure-ment of the initial opening. An initial crack length of 30 mm gives an acceptable
com-promise between stiffness and accuracy: KE¼ 150 N=mm with an
uncertainty lower than 20% for G ¼ 100 N=m. To have a crack opening indicator, an electrical contactor was fixed at the end of
the specimen (Fig. 10).
Fig. 8. Cinematic scheme of the mechanical test device.
3.2. Experimental conditions and test procedure
3.2.1. Mean cycle fatigue loading value adjustment: Fmean
The adjustment of the initial position is described by the
follow-ing equation (Fig. 8):
Fmoy¼ KE d ¼ ÿM g ÿ KR
D
l ð7ÞAs the principal axis is rigidly linked to the specimen, the crack opening d imposed on the specimen is measured with the help of a displacement laser sensor pointed at the top surface of this axis (Fig. 11). The opening measurement begins as soon as the opening
contactor is activated (see also10). This initial equilibrium position
is fixed with a lock nut.
3.2.2. Cycle fatigue loading amplitude adjustment: Famp
System dynamics. The damped system dynamics without load-ing is described as follows:
M €umþ C _umþ Ktum¼ 0 ð8Þ
€
umþ 2nr
x
ru_mþx
2rum¼ 0 ð9ÞWith um the mass displacement, Kt¼ KEþ KR the equivalent
spring stiffness and nrthe reduced damping like:
nr¼ C 2 ffiffiffiffiffiffiffiffiffiffiK tM p 1 ð10Þ and
x
rlike:x
r¼ 2p
fr ð11ÞWith frthe resonance frequency of the system.
The natural pseudo angular frequency of the system is then:
-
r¼x
r ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ÿ n2 r qx
r¼ ffiffiffiffiffi Kt M r ð12ÞThe global system dynamics subject to the shaker acceleration are then governed by the following equation:
M€u þ C _u þ Ktu ¼ ÿM €up ð13Þ
with u the mass displacement relative to the and up the shaker
displacement.
Placing this in the Laplace domain:
U
x
2M þ ix
C þ K t ÿ¼
x
2M Up ð14Þ
with
x
the angular frequency of the system excitation.The transfer function of the system acceleration is:
Hð
x
Þ ¼UU€ p¼x
2M ÿx
2M þ ix
C þ K t¼ x xr 2 1 þ 2inrxxrÿ xxr 2 ð15ÞFrom this equation are taken:
the absolute value of the amplification factor of the mass rela-tive to the shaker, and
the phase (/) which at the resonant frequency is equal to
/r¼ ÿ90
A frequency sweeping test is therefore necessary to determine the resonant frequency of the global system and the amplification factor associated with it. This allows to calculate the acceleration value needed to control the shaker in order to get the desired accel-eration of the mass.
FampControl.
The mass displacement is deduced from its acceleration:
€ u ¼
c
:sinðx
t þ /Þ u ¼ ÿ c x2sinðx
t þ /Þ ( ð16ÞThe load applied on the specimen is:
Famp sinð
x
t þ /Þ ¼ ÿKE u ¼ KEc
x
2sinðx
t þ /Þ ¼ KE Hðx
Þ j jc
px
2 sinðx
t þ /Þ ð17ÞIt was decided to directly control the mass acceleration
ampli-tude, M (
c
), instead of the amplitude of the shaker acceleration(
c
p) which is usually the case. This has the advantage of avoidingany accurate measurement of the system transfer function, the mass-spring-specimen, which revealed a bit delicate to achieve. In-deed it is sensitive to the sweeping speed, and friction caused by the guiding rails leads to some difficulties in the very low range
of imposed acceleration. The amplitude of acceleration
c
cis thenimposed during loading and results in an accurate value for the
load on the DCB specimen (Eq. (18)).
Famp¼ KE
c
cx
2 ð18Þ3.2.3. Operating conditions in fatigue
The fatigue test to determine the threshold for crack propaga-tion must be performed at a fixed load level and a given load ratio R (Fig. 9). Firstly the average load level on the specimen Fmeanis
completely defined by the initial load imposed by the spring (Part
3.2.1). Indeed it is not modified by the specimen stiffness change when the delamination propagates during the fatigue test.
Sec-ondly in order to fix the load ratio during the fatigue test, Famp
has to be kept constant (Eq. (6)). These conditions must be held
during the propagation of the crack until the defined stopping cri-terion is reached.
It was decided to follow the evolution of the resonant frequency during the fatigue test; it has two advantages when the crack propagates.
It allows to follow the crack progress and to define a test stop-ping criterion.
When the delamination crack propagates, the opening stiffness
of specimen decreases with the resonance frequency[24]. The
curve of the transfer function is shifted to lower frequencies. If the loading was performed at fixed frequency, the
amplifica-tion factor would also decrease (Fig. 12). Thus, as the test is
con-trolled by the relative acceleration of the mass, the acceleration
imposed by the shaker should increase to meet
c
c. This increaseof input acceleration would be the unique indicator of the pro-gress of the crack which would be difficult to quantify precisely. For a loading which follows the resonant frequency, the input frequency adapts to lock itself to the resonant frequency by
keeping the phase of the transfer function equal to ÿ90(Part
3.2.2). The change in input frequency is then directly linked to the change in stiffness of the specimen; and this later very eas-ily linked to the crack extension through the compliance law (Fig. 3). The stopping frequency of the test is calculated to get a stiffness reduction of the specimen of about 5% as it is
recom-mended in the standard fatigue test[3]. In this study the
fre-quency shift is around 1.5 Hz corresponding to a propagation of 0.5 mm for the test specimens.
It compensates the reduction in stiffness to keep Fampalmost
constant
When the delamination propagates, the opening specimen
stiff-ness KEand the resonant frequency
x
rdecreases in theexpres-sion of Famp(Eq. (18)). But this resonant frequency is changing
with KEand so it comes at the resonance that:
Famp¼ KE
c
cx
2 r ¼ KE KtMc
c¼ KE KEþ KRMc
c ð19ÞThe reduction in stiffness is then largely compensated. To strictly
obtain a constant Famp;
c
cshould be adapted as well. But it revealsFig. 14. G–N propagation curve: 10 Hz and 100 Hz.
Fig. 15. SEM fracture surfaces for 10 Hz and 100 Hz (from left to right). Fig. 13. G–N curve at 100 Hz with and without the load sensor.
to be complex to set up for a limited accuracy gain. Indeed, without
any adjustment of
c
c, this leads to less than 1% of error for Famp.3.2.4. Test facilities and operating process
The tests were performed on a shaker (Fmax¼ 40 kN in sinus) of
the DGA Techniques Aeronautiques test center. Two accelerome-ters were used to track accelerations of the mass and shaker. A voltage subtractor was used to measure the relative acceleration of the mass compared with the shaker which is the parameter
con-trolled during tests
c
c. The data recorded during the test were: theamplitude of the relative acceleration of the mass and the fre-quency. The crack propagation was followed through the monitor-ing of the resonance frequency of the system. As seen before this frequency is linked to the opening stiffness of the specimen and then by the compliance law to the delamination size. In order to evaluate the specimen self-heat generation, specimen temperature evolutions were monitored with a thermal middle wavelength
camera (sensitivity between 3 and 5
l
m) on the entire sampleand also near the crack tip.
The tests were thus controlled by setting the relative accelera-tion of the mass M at a constant value while following the resonant frequency of the system.
Once the initial opening was set, a frequency sweep was carried out at low acceleration to measure the resonant frequency of the global system and the amplification factor. Knowing the size of the initial crack and thus the specimen’s initial stiffness, the appar-ent mass set in motion by the system was precisely calculated (this mass partially depends on the installation conditions). The
acceler-ation
c
cnecessary to impose the desired loading was thencalcu-lated (Eq. (19)). The minimum acceleration required to be
imposed to the shaker was determined with the amplification
fac-tor and ensured
c
cto be obtained.The fatigue test was then run and stopped when the final fre-quency was reached (Part 3.2.3). As for the classical tests, the data recorded during test were used to plot the G–N propagation curve
with the ERR calculation compliance method (Eq. (3), Part2.3.2).
For some specimens, the dynamic test device was improved by adding a piezoelectric load sensor under the loading axis. The zero
sensor was adjusted before setting the specimen. Fmeanand Famp
were then controlled using the sensor information which quite
Fig. 16. One cycle opening displacement and speed for 10 Hz and 100 Hz (from left to right).
simplify the process. As shown in theFig. 13, both experimental re-sults are in good agreement.
3.3. Results comparison 3.3.1. Frequency effect
The results are presented in the form of G–N curve to compare the fatigue propagation growth onset. Indeed, this data reduction is more suitable for dynamical test since a delamination propagation lead to a shift in frequency. So Paris tests cannot be performed for a long range of crack propagation when assuming a constant frequency.
The propagation thresholds obtained from the tests at 100 Hz
are lower than those found at 10 Hz (Fig. 14). As the frequency
in-creases, the strength of the material to crack propagation seems to decrease. Temperature specimen evolution due to vibrations at 100 Hz was monitored during fatigue and did not show significant heating of the material (relative change of temperature below 1 °C at the crack tip). So the behavior difference between the two quencies cannot be explained by a temperature increase. The fre-quency effect seems more likely to be linked with a loading rate
effect[16]: when loading at 100 Hz the strain rate applied to the
material is greater than for 10 Hz. This strain rate rise can explain
the decrease in fatigue crack growth resistance[23,25].
The SEM fracture surfaces of 10 Hz specimen and 100 Hz
spec-imen are rather similar (Fig. 15top). Many thermoplastic nodules
added to increase the composite matrix toughness are distinctly observed for the largest magnification. The only tiny difference be-tween specimen takes place in the thermoplastic nodules fracture surface, which seem to present plastic deformation (white tips on
the nodule surface) for the 10 Hz specimens (Fig. 15bottom-left)
whereas the 100 Hz specimens nodules have a matt aspect (Fig. 15bottom-right). This might be associated with the material
rate dependency reported in part2.2.
3.3.2. Strain rate effect
During the cycling the specimen opening displacement and speed are in phase quadrature: when the displacement is maximal the speed is equal to zero. In order to compare the two frequency tests, ERR and speed were plotted for the maximal and minimal ERR of the G–N curve ranges (10 Hz :¼ ½112 N=m; 286 N=m;
100 Hz :¼ ½80 N=m; 166 N=mÞ (Fig. 16). The maximal
displace-ment corresponds to the maximal ERR imposed in the cycle, that is where the fatigue cycling is the most efficient. The rates calcu-lated around this ERR peak are greater for 100 Hz than for
10 Hz : 1 eÿ4second before the maximal displacement, the opening
speeds for 10 Hz tests are between 0.207 mm/s and 0.331 mm/s whereas the ones for 100 Hz tests range between 6.58 mm/s and 9.48 mm/s.
To take into consideration the material rate dependency (Part
2.2), the ERR used for plotting the G–N curve is adimensioned by
GIstat
p in the 10 Hz test case and by GIdynp in the 100 Hz one
(Fig. 17). The two G–N curves are similar which confirms that this frequency effect is linked to a rate effect. The fatigue delamination growth onset of a material can then be determined with the new test in resonance taking into consideration this rate effect. The main G–N curve characterizing the material in fatigue was found to follow a log-linear law:
Gmax
GIp ¼ 1:6 N ÿ0:13
c ð20Þ
4. Conclusions
A new dynamical fatigue test at resonance has been developed for propagation test in mode I. This system based on DCB specimen
is a dynamic mass-spring-specimen that is designed to resonate. The defined methodology allows a reproducible stopping condition identical to standard tests that are performed at lower frequencies (10 Hz). For now the device sizing limits the resonant frequency of the system to around 100 Hz. This test frequency prevents from reaching gigacycle within a reasonable test duration. In order to obtain higher frequencies, the device should be improved by reducing the mass weight and the friction in the axis guide. Never-theless, this system enabled to perform resonance DCB fatigue test at high frequency without heat generation (no more than 1 °C) and to proceed to the fatigue characterization of a laminate composite material.
As reference standard fatigue tests in mode I at 10 Hz were con-ducted to determine the Paris law and fatigue propagation growth onset curve (G–N). A new data reduction was settled to allow plot-ting a G–N curve with Paris results which matches with the stan-dard one. Comparison of results between the tests at different frequencies highlighted a frequency effect which was found to be likely due to a rate effect. By using adimensional ERR values taking into consideration the distinct dynamical and static propagation
ERR, G–N curves at both frequencies were unified (Eq. (20)). Then,
the dynamical test method allows to obtain a trustworthy G–N curve by reducing the time taken by a factor of ten.
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